A009973 Powers of 29.

1, 29, 841, 24389, 707281, 20511149, 594823321, 17249876309, 500246412961, 14507145975869, 420707233300201, 12200509765705829, 353814783205469041, 10260628712958602189, 297558232675799463481, 8629188747598184440949

Offset: 0

Author

N. J. A. Sloane, Dec 11 1996

Keywords

• nonn
• easy

Comments

Same as Pisot sequences E(1, 29), L(1, 29), P(1, 29), T(1, 29). Essentially same as Pisot sequences E(29, 841), L(29, 841), P(29, 841), T(29, 841). See A008776 for definitions of Pisot sequences.

The compositions of n in which each natural number is colored by one of p different colors are called p-colored compositions of n. For n>=1, a(n) equals the number of 29-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011

Numbers n such that sigma(29*n) = 29*n + sigma(n). - Jahangeer Kholdi, Nov 23 2013

Links

• T. D. Noe, Table of n, a(n) for n = 0..100
• Tanya Khovanova, Recursive Sequences
• Index entries for linear recurrences with constant coefficients, signature (29).

Programs

Magma

[29^n: n in [0..30]]; // Vincenzo Librandi, Nov 21 2010

Maple

A009973:=n->29^n; seq(A009973(n), n=0..20); # Wesley Ivan Hurt, Jun 06 2014

Mathematica

29^Range[0,20] (* Harvey P. Dale, Jul 19 2011 *)

Maxima

makelist(29^n, n, 0, 30); /* Martin Ettl, Nov 07 2012 */

PARI

a(n)=29^n \\ Charles R Greathouse IV, Sep 24 2015

Sage

[29^n for n in (1..17)] # Zerinvary Lajos, Apr 29 2009

Formula

G.f.: 1/(1-29*x). - Philippe Deléham, Nov 24 2008

a(n) = 29^n; a(n) = 29*a(n-1) for n>0, a(0)=1. - Vincenzo Librandi, Nov 21 2010

G.f.: (G(0)-2)/(9*x), where G(k)= 1 + 1/(1 - x*(9*k-9)/(x*(9*k+20) - 2/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 17 2013